(1),(2,4),(5,7,9,1)(0,20,22),(31,33,35,3)(6,40,42,44,46),(51,53,55,57,59),(60,62,64,66,68,80,82,84,86,88)... Those runs of equal parity digits are of length 1,2,4,5,7,9,10,20... which is the sequence itself.